Perfect simulation for sample-based inference

Perfect simulation algorithms based on Propp and Wilson (1996) have so far been of limited use for sampling problems of interest in statistics. We specify a new family of perfect sampling algorithms obtained by combining MCMC tempering algorithms with dominated coupling from the past, and demonstrate that our algorithms will be useful for sample based inference. Perfect tempering algorithms are less efficient than the MCMC algorithms on which they typically depend. However, samples returned by perfect tempering are distributed according to the intended distribution, so that these new sampling algorithms do not suffer from the convergence problems of MCMC. Perfect tempering is related to rejection sampling. When rejection sampling has been tried, but has proved impractical, it may be possible to convert the rejection algorithm into a perfect tempering algorithm, with a significant gain in algorithm efficiency.